How do I remove the personal hotspot blue bar?

As long as you have something connected to the Personal Hotspot, that blue bar will be there, just as, as long as your actively navigating to a destination, but not in the Maps app, the green bar will be there. You can't turn them off.

Submit your feedback directly to Apple using the appropriate link on the Feedback page:

http://www.apple.com/feedback

How do I remove the horizontal blue line on top of my screen